The booking is administered online, just like the survey. The editors who have write access on the page have the right to administer the booking.
If you are logged in as a user with booking page permissions, all settings you have set are ignored. Therefore, if you want to test the settings, you can go to the page without a role with administrator rights.
In this example, your own bookings are marked blue and other people's bookings yellow. Times that cannot be booked are marked black.
To see who made the other booking, you can hover the cursor over the yellow field.
The page published: 2019-01-07